A numerical study on the fluid compressibility effects in strongly coupled fluid–solid interaction problems
Pages 1205 - 1217
Abstract
Interactions between an incompressible fluid passing through a flexible tube and the elastic wall is one of the strongly coupled fluid–solid interaction (FSI) problems frequently studied in the literature due to its research importance and wide range of applications. Although incompressible fluid is a prevalent model in many simulation studies, the assumption of incompressibility may not be appropriate in strongly coupled FSI problems. This paper narrowly aims to study the effect of the fluid compressibility on the wave propagation and fluid–solid interactions in a flexible tube. A partitioned FSI solver is used which employs a finite volume-based fluid solver. For the sake of comparison, both traditional incompressible (ico) and weakly compressible (wco) fluid models are used in an Arbitrary Lagrangian–Eulerian (ALE) formulation and a PISO-like algorithm is used to solve the unsteady flow equations on a collocated mesh. The solid part is modeled as a simple hyperelastic material obeying the St-Venant constitutive relation. Computational results show that not only use of the weakly compressible fluid model makes the FSI solver in this case more efficient, but also the incompressible fluid model may produce largely unrealistic computational results. Therefore, the use of the weakly compressible fluid model is suggested for strongly coupled FSI problems involving seemingly incompressible fluids such as water especially in cases where wave propagation in the solid plays an important role.
Article highlights
•
Flow in a flexible tube is a strongly coupled FSI problem.
•
The weakly compressible fluid model has computational merits in FSI problems.
•
The incompressibility assumption for liquids leads to unrealistic results in some FSI cases.
References
[1]
Gerbeau J-F and Vidrascu M A quasi-newton algorithm based on a reduced model for fluid–structure interaction, problems in blood flows Math Model Numer Anal 2003 37 631-647
[2]
Causin P, Gerbeau J-F, and Nobile F Added-mass effect in the design of partitioned algorithms for fluid-structure problems Comput Methods Appl Mech Eng 2005 194 4506-4527
[3]
Förster C, Wall WA, and Ramm E Artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows Comput Methods Appl Mech Eng 2007 196 1278-1293
[4]
Badia S, Quaini A, and Quarteroni A Modular vs non-modular preconditioners for fluid-structure systems with large added-mass effect Comput Methods Appl Mech Eng 2008 197 4216-4232
[5]
He T Partitioned coupling strategies for fluid–structure interaction with large displacement: explicit, implicit and semi-implicit schemes Wind Struct 2015 20 3 423-448
[6]
Le Tallec P and Mouro J Fluid structure interaction with large structural displacements Comput Methods Appl Mech Eng 2001 190 3039-3067
[7]
De Santiago E and Law KH A robust distributed adaptive finite element program for coupled fluid-structure problems Eng Comput 1999 15 137-154
[8]
Parker G, Guilkey J, and Harman T A component-based parallel infrastructure for the simulation of fluid–structure interaction Eng Comput 2006 22 277-292
[9]
Deiterding R, Radovitzky R, Mauch SP, Noels L, Cummings JC, and Meiron DI A virtual test facility for the efficient simulation of solid material response under strong shock and detonation wave loading Eng Comput 2006 22 325-347
[10]
Degroote J, Swillens A, Bruggeman P, Haelterman R, Segers P, and Vierendeels J Simulation of fluid–structure interaction with the interface artificial compressibility method Int J Numer Methods Biomed Eng 2010 26 276-289
[11]
Raback P, Jarvinen E, Ruokolainen J (2008) Computing the artificial compressibility field for partitioned fluid–structure interaction simulations. Eighth World Congress on Computational Mechanics, 5th European Congress on computational methods in applied sciences and engineering, Venice, Italy
[12]
Bogaers AEJ, Kok S, Reddy BD, and Franz T Extending the robustness and efficiency of artificial compressibility for partitioned fluid–structure interactions Comput Methods Appl Mech Eng 2015 283 1278-1295
[13]
He T, Wang T, and Zhang H The use of artificial compressibility to improve partitioned semi-implicit fsi coupling within the classical chorin-témam projection framework Comput Fluids 2018 166 64-77
[14]
Marrone S, Colagrossi A, Di Mascio A, and Le Touzé D Prediction of energy losses in water impacts using incompressible and weakly compressible models J Fluids Struct 2015 54 802-822
[15]
Andersson H, Nordin P, Borrvall T, Simonsson K, Hilding D, Schill M, Krus P, and Leidermark D A co-simulation method for system-level simulation of fluid-structure couplings in hydraulic percussion units Eng Comput 2017 33 317-333
[16]
Chorin AJ A numerical method for solving incompressible viscous flow problems J Comput Phys 1967 2 12-26
[17]
Pierre B, Oger G, Guilcher P, and Touze DL A weakly-compressible cartesian grid approach for hydrodynamic flows Comput Phys Commun 2017 220 31-43
[18]
Seo JH and Moon YJ Linearized perturbed compressible equations for low mach number aeroacoustics J Comput Phys 2006 218 702-719
[19]
Hirt CW, Amsden AA, and Cook JL An arbitrary Lagrangian–Eulerian computing method for all flow speeds J Comput Phys 1974 14 3 227-253
[20]
Hughes THR, Liu WK, and Zimmermann TK Lagrangian–Eulerian finite element formulation for incompressible viscous flow Comput Methods Appl Mech Eng 1981 29 329-349
[21]
Barlowa AJ, Maire PH, Rider WJ, Rieben RN, and Shashkov MJ Arbitrary Lagrangian–Eulerian methods for modeling high-speed compressible multimaterial flows J Comput Phys 2016 322 603-665
[22]
Greenshields CJ, Weller HG, and Ivankovic A The finite volume method for coupled fluid fow and stress analysis Comput Model Simul Eng 1999 4 213-218
[23]
Kochupillai J, Ganesan N, and Padmanabhan C A new finite element formulation based on the velocity of flow for water hammer problems Int J Press Vessels Pip 2005 82 1-14
[24]
Daude F, Tijsseling AS, and Galon P Numerical investigations of water-hammer with column- separation induced by vaporous cavitation using a one-dimensional finite-volume approach J Fluids Struct 2018 83 91-118
[25]
Formaggia L, Gerbeau JF, Nobile F, and Quarteroni A On the coupling of 3D and 1D Navier–Stokes equations for flow problems in compliant vessels Comput Methods Appl Mech Eng 2001 191 6–7 561-582
[26]
Gee MW, Küttler U, and Wall WA Truly monolithic algebraic multigrid for fluid–structure interaction Int J Numer Meth Eng 2011 85 987-1016
[27]
Eken A and Sahin M A parallel monolithic algorithm for the numerical simulation of large-scale fluid structure interaction problems Int J Numer Meth Fluids 2016 80 687-714
[28]
Lozovskiya A, Olshanskii MA, and Vassilevski YV Analysis and assessment of a monolithic FSI finite element method Comput Fluids 2019 179 277-288
[29]
Soloukhin RI (1966) Shock waves and detonations in gases. Mono Books
[30]
Zhang G, Setoguchi T, and Kim HD Numerical simulation of flow characteristics in micro shock tubes J Therm Sci 2015 24 3 246-253
[31]
Prandtl L Uber die ausgebildete Turbulenz ZAMM 1925 5 136-139
[32]
Issa RI Solution of implicitly discretized fluid flow equations by operator-splitting J Comput Phys 1985 62 40-65
[33]
Jang DS, Jetli R, and Acharya S Comparison of the PISO, SIMPLER and SIMPLEC algorithms for the treatment of the pressure-velocity coupling in steady flow problems Numer Heat Transf 1986 10 209-228
[34]
Greenshields CJ and Weller HG A unified formulation for continuum mechanics applied to fluid–structure interaction in flexible tubes Int J Numer Meth Eng 2005 64 1575-1593
[35]
Demirdzic I and Peric M Space conservation law in finite volume calculations of fluid flow Int J Numer Meth Fluids 1988 8 1037-1050
[36]
Maneeratana K (2000) Development of finite volume method for non-linear structure applications. PhD Thesis, Department of Mechanical Engineering Imperial College of Science, Technology and Medicine, London
[37]
Jasak H and Tukovic Z Upadted lagrangian finite volume solver for large deformation dynamic response of elastic Trans FAMENA 2007 31 1 55-70
[38]
Donea J, Huerta A, Ponthot J-Ph, Rodriguez-Ferran A (2004) Arbitrary Lagrangian–Eulerian methods. Encyclopedia of computational mechanics; Chapter 14
[39]
Ryzhakov P, Marti J, Idelsohn S, and Oñate E Fast fluid–structure interaction simulations using a displacement-based finite element model equipped with an explicit streamline integration prediction Comput Methods Appl Mech Eng 2017 315 1080-1097
[40]
Mok D and Wall WA Wall WA, Bletzinger KU, and Schweitzerhof K Partitioned analysis schemes for the transient interaction of incompressible flows and nonlinear flexible structures Trends in computational structural mechanics 2001 Barcelona CIMNE
[41]
Küttler U and Wall WA Fixed-point fluid–structure interaction solvers with dynamic relaxation Comput Mech 2008 43 61-72
[42]
Pielhop K, Klaas M, and Schröder W Experimental analysis of the fluid–structure interaction in finite-length straight elastic vessels Eur J Mech B/Fluids 2015 50 71-88
[43]
Geoghegan PH, Buchmann NA, Soria PHG, and Jermy MC Time-resolved PIV measurements of the flow field in a stenosed, compliant arterial model Exp Fluids 2013 54 1528
[44]
Tijsseling AS Water hammer with fluid–structure interaction in thick-walled pipes Comput Struct 2007 85 844-851
Index Terms
- A numerical study on the fluid compressibility effects in strongly coupled fluid–solid interaction problems
Index terms have been assigned to the content through auto-classification.
Recommendations
Particle-based realistic simulation of fluid–solid interaction
In this paper a novel method for simulating incompressible viscous fluid and solid coupling is presented. In the coupling model, a rigid object is treated as a special fluid constrained to rigid body motion. To animate the coupling model, the Smoothed ...
Improved PISO algorithms for modeling density varying flow in conjugate fluid-porous domains
Two modified segregated PISO algorithms are proposed, which are constructed to avoid the development of spurious oscillations in the computed flow near sharp interfaces of conjugate fluid-porous domains. The new collocated finite volume algorithms ...
Preconditioning for incompressible flows with free-surfaces and two-fluid interfaces
We investigate preconditioners for solving steady or implicit-unsteady arbitrary-Lagrangian-Eulerian moving-mesh formulations of incompressible free-surface and interfacial flow problems. The solution for the flow is obtained using the artificial ...
Comments
Information & Contributors
Information
Published In
© Springer-Verlag London Ltd., part of Springer Nature 2019.
Publisher
Springer-Verlag
Berlin, Heidelberg
Publication History
Published: 01 April 2021
Accepted: 22 October 2019
Received: 23 June 2019
Author Tags
Qualifiers
- Research-article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 16 Nov 2024
Other Metrics
Citations
View Options
View options
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in